With the aim of understanding the mechanisms of evolution of genes and populations and of maintenance of genetic variability within populations, two mutually related research projects with emphasis on molecular aspects are proposed. (1) Differentiation of genes and populations. Mathematical theories of the relationship between the phylogeny of genes and the phylogeny of species and of the evolution of reproductive isolation in speciation will be developed. Statistical methods of constructing phylogenetic trees or dendrograms from molecular data will also be studied, and an attempt will be made to find the most efficient method of obtaining the correct phylogenetic tree. To understand the mechanism of concerted evolution of multigene families, phylogenetic analyses of DNA sequences will be conducted for various multigene families such as the T-cell receptor, MHC, and immunoglobulin families. An effort will also be made to collect gene frequency data for as many genetic loci as possible for about 50 representative human races (populations), and the pattern and mechanism of evolution of human populations will be investigated. (2) Genetic variability and its maintenance. Mathematical theories for evaluating the effects of overdominant and purifying selection on the extent of genetic variability among member genes of a multigene family and the coalescence time of polymorphic alleles within populations will be developed. Mathematical studies will also be made to develop a method of estimating the recombination value between two linked blocks of restriction enzyme cleavage sites in DNA and the expected relationship between the number of heterozygous loci and growth rate. The mathematical theories obtained will then be applied to analyze data from various organisms. In addition to the above studies, statistical analysis of polymorphic DNA sequences will be made to investigate the mechanism of maintenance of DNA polymorphism.